R-INLA
In this practical you will use R (R Core Team 2019) as well as INLA
to carry out a spatial and a spatio-temporal small area disease risk
analysis.
In particular, you are going to model yearly hospital admissions for respiratory conditions (ICD-10 codes: J00-J99) in the Greater Glasgow and Clyde health board, for the period 2007 - 2011.
Scotland is divided into 14 health boards, and here we focus on the Greater Glasgow and Clyde health board, which contains the city of Glasgow and has a population of around 1.2 million people, during the period 2007 to 2011. This health board is split into N = 271 intermediate geographies (IG), which are a key geography for the distribution of small-area statistics in Scotland and contain populations of between 2,468 and 9,517 people.
The data used in this practical are freely available from the R
package CARBayesST (Lee, Rushworth,
and Napier 2018). A subset of these data is in the file
RESP_DATA.csv.
library(dplyr) # A package for data manipulation
library(sf) # Simple feature for R
library(spdep) # Functions and tests for evaluating spatial patterns
# and autocorrelation
library(tidyr)
library(INLA) # Integrated Nested Laplace Approximation package
library(ggplot2) # A package that implements the grammar of graphics, which is a term used to
# break up graphs into semantic components, such as geometries and layers.
library(viridis) # A package providing color palettes
library(patchwork)
# For tables in RMarkdown
library(knitr)
library(kableExtra)
.csv file with the data and call the
data.frame object as RESP_DATA.RESP_DATA <- read.csv("RESP_DATA.csv", header=TRUE)
Here The first column labelled IG is the set of unique
identifiers for each IG, year is the year of
hospitalization, while observed and expected
are respectively the observed and expected numbers of hospital
admissions due to respiratory diseases.
kable(RESP_DATA %>%
group_by(year) %>%
summarise(observed = sum(observed), expected=sum(expected)), booktabs = T, caption = "Hospital admissions by year") %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "center")
| year | observed | expected |
|---|---|---|
| 2007 | 20410 | 23727.31 |
| 2008 | 21960 | 24955.70 |
| 2009 | 21166 | 24206.05 |
| 2010 | 21234 | 26007.28 |
| 2011 | 22548 | 26234.11 |
Note: to know more about this function, you can type in the console
?knitr::kable and visit the page https://haozhu233.github.io/kableExtra/awesome_table_in_pdf.pdf
st_read from sf package and call the object as
GGHB.GGHB <- st_read("GGHB.shp")
## Reading layer `GGHB' from data source
## `/Users/marta/Dropbox/Books/INLABook/ShortCourse/VIBASS/Practicals/Practical2/GGHB.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 271 features and 3 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: 218820 ymin: 644792 xmax: 272283 ymax: 689565
## CRS: NA
ggplot2 package.ggplot() +
geom_sf(data = GGHB, color = "blue", fill = "white") +
coord_sf() + #axis limits and CRS
theme_bw() + # dark-on-light theme
theme(axis.title = element_text(size = 14),
axis.text = element_text(size = 12))
The figure shows that the river Clyde partitions the study region into a northern and a southern sub-region, and no areal units on opposite banks of the river border each other. We will account for this issue when creating neighbors for the areal units.
In order to use the same data structure for both the space-only model and later the space-time model, a new set of data is formed by aggregating both the observed and expected counts over time. A Poisson-log linear model is then fitted, assuming a BYM2 model for the random effects. Let each areal unit \(i\) be indexed by the integers \(1, 2,...,N\). \[ \begin{eqnarray} O_{i}|\lambda_{i} & \sim & \text{Poisson}(\lambda_{i}E_{i} ) \\ \log(\lambda_{i}) & = & \alpha + \theta_{i} + \phi_{i} \\ \theta_{i} & \sim & N(0, \sigma_{\theta}^2)\\ {\bf \phi} & \sim & \hbox{ICAR}({\bf W}, \sigma_{\phi}^2)\\ \alpha & \sim & \text{Uniform}(-\infty, +\infty) \\ 1/\sigma_{\theta}^2 & \sim & \text{Gamma}(1,0.001) \\ 1/\sigma_{\phi}^2 & \sim & \text{Gamma}(0.5,0.005) \\ \end{eqnarray} \]
snap argument (boundary points less than snap distance
apart are considered to indicate contiguity; see https://cran.r-project.org/web/packages/spdep/vignettes/nb.pdf)GGHB_nb <- poly2nb(GGHB, snap=1000, queen=TRUE)
summary(GGHB_nb)
## Neighbour list object:
## Number of regions: 271
## Number of nonzero links: 3414
## Percentage nonzero weights: 4.64863
## Average number of links: 12.59779
## Link number distribution:
##
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 23 25 27 33
## 1 4 6 7 6 11 16 12 17 8 18 15 27 21 23 18 19 17 7 6 4 5 1 1 1
## 1 least connected region:
## 202 with 1 link
## 1 most connected region:
## 234 with 33 links
Convert the list of neighbors to inla format using the
function nb2WB().
nb2INLA("GGHB.graph",GGHB_nb)
GGHB.adj <- paste(getwd(),"/GGHB.graph",sep="")
RESP_DATA %>% group_by(SP_ID) %>%
summarize(observed = sum(observed),
expected = sum(expected)) %>%
dplyr::rename(O = observed, E = expected) -> RESP_DATAagg
RESP_DATAagg %>% mutate(SMR = O/E) -> RESP_DATAagg
ggplot2 package. For the map use the following breakpoints
[min,0.4], (0.4-0.6], (0.6-0.8], (0.8,1], (1,1.2], (1.2-1.4], (1.4-1.6],
(1.6-max].Remember that, before to produce the map, you need to join the
sf object and the data frameRESP_DATAagg. To
do so you can use the function left_join from the library
dplyr (see previous practicals).
RESP_DATAagg$SMRcat <- cut(RESP_DATAagg$SMR,
breaks=c(min(RESP_DATAagg$SMR),
0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6,
max(RESP_DATAagg$SMR)), include.lowest = T)
map_SMR <- left_join(GGHB, RESP_DATAagg, by = c("SP_ID" = "SP_ID"))
and plot:
ggplot() + geom_sf(data = map_SMR, col = NA) + aes(fill = SMRcat) +
theme_bw() + scale_fill_viridis_d() +
guides(fill=guide_legend(title="SMR"))
Map of the average SMRs over the period 2007-2011
INLAID<- seq(1,271)
formula_BYM2 <- O ~ f(ID, model="bym2", graph=GGHB.adj,
hyper=list(prec = list(
prior = "pc.prec",
param = c(0.5 / 0.31, 0.01)),
phi = list(
prior = "pc",
param = c(0.5, 2 / 3))))
sBYM.model <- inla(formula=formula_BYM2, family="poisson", data=RESP_DATAagg, E=E, control.compute=list(dic=TRUE, waic=TRUE))
#Relative risks
RR_sBYM<-c()
for(i in 1:271){
RR_sBYM[i] <- inla.emarginal(function(x) exp(x),
sBYM.model$marginals.random$ID[[i]])
}
#Posterior probabilities
RR_sBYM_marg <- sBYM.model$marginals.random$ID[1:271]
PP_sBYM <- lapply(RR_sBYM_marg, function(x) {1-inla.pmarginal(0,x)})
resRR_PP <- data.frame(resRR=RR_sBYM,
PP=unlist(PP_sBYM),
SP_ID=RESP_DATAagg[,1])
ggplot2 package, produce a map of the posterior
mean of the residual RRs and the posterior probabilities that the
residual RRs are > 1resRR_PP$resRRcat <- cut(resRR_PP$resRR, breaks=c(min(resRR_PP$resRR),
0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6,
max(resRR_PP$resRR)),include.lowest = T)
PP that the residual
RRs is > 1, use the following breakpoints [0-0.2], (0.2-0.8],
(0.8-1].# breakpoints
resRR_PP$PPcat <- cut(resRR_PP$PP, c(0, 0.2, 0.8, 1.00), include.lowest = TRUE)
sf object and data frame with the
posterior estimatesmap_RR_PP <- left_join(GGHB, resRR_PP, by = c("SP_ID" = "SP_ID"))
PP using ggplot2
package.ggplot() + geom_sf(data = map_RR_PP) + aes(fill = resRRcat) +
theme_bw() + scale_fill_brewer(palette = "PuOr") +
guides(fill=guide_legend(title="RR")) + ggtitle("RR Spatial model") +
theme(text = element_text(size=15),
axis.text.x = element_blank(),
axis.text.y = element_blank(), plot.title = element_text(size = 12, face = "bold")
)-> p1
ggplot() + geom_sf(data = map_RR_PP) + aes(fill = PPcat) +
theme_bw() +
scale_fill_viridis(
option = "plasma", name="PP",
discrete = T,
direction = -1,
guide = guide_legend(
title.position = 'top',
reverse = T
)) + ggtitle("PP Spatial model") + theme(text = element_text(size=15),
axis.text.x = element_blank(),
axis.text.y = element_blank(), plot.title = element_text(size = 12, face = "bold")
) -> p2
p1|p2
As the BYM2 has the structured (CAR) and unstructured (iid)
components it might be useful to get some ideas about the strength of
the spatially structured components as this would indicate the level of
clustering in the data. To do so we ca simply obtain the posterior
summary of the phi hyperparameter
sBYM.model$summary.hyperpar
## mean sd 0.025quant 0.5quant 0.975quant mode
## Precision for ID 7.6801757 0.8105148 6.1734660 7.6512274 9.362810 NA
## Phi for ID 0.6716711 0.1257730 0.4069953 0.6802351 0.887077 NA
This tells us that about 2/3 of the spatial variability is explained by the spatially structured component - which makes sense if we look at the map of the RR, which show a degree of spatial clustering.
Now, we extend the above analysis to a separable space-time model without interactions. For the temporal component, we use the specification introduces in the lecture with a temporal unstructured random effect and a structured one (RW1 prior).
Let each areal unit \(i\) be indexed
by the integers \(1, 2,...,N\). As in
the spatial case, we use a Poisson distribution to model the number of
hospital admission \(O_it\), in area
\(i\) at time \(t\). The mathematical specification of the
model includes now an additional temporal dependence term, which can be
modeled using a non-stationary random walk prior: ${i} ({i-1},
^2_{}).
The model implement in this practical assumes no space-time interaction
and a spatial convolution with random walk in time:
\[ \begin{eqnarray} O_{i}|\lambda_{i} & \sim & \text{Poisson}(\lambda_{i}E_{i} ) \\ \log(\lambda_{i}) & = & \alpha + \theta_{i} + \phi_{i} + \xi_t + \gamma_t \\ \theta_{i} & \sim & N(0, \sigma_{\theta}^2)\\ {\bf \phi} & \sim & \hbox{ICAR}({\bf W}, \sigma_{\phi}^2)\\ \gamma_t &\sim & N(0, \sigma_{\gamma}^2) \\ \xi_t & \sim & RW1(\sigma_{\xi}^2) \\ \alpha & \sim & \text{Uniform}(-\infty, +\infty) \\ 1/\sigma_{\theta}^2 & \sim & \text{Gamma}(1,0.001) \\ 1/\sigma_{\phi}^2 & \sim & \text{Gamma}(0.5,0.005) \\ 1/\sigma_{\gamma}^2 & \sim & \text{Gamma}(1,0.001) \\ 1/\sigma_{\xi}^2 & \sim & \text{Gamma}(0.5,0.005) \\ \end{eqnarray} \]
#Join the data with the shapefile so the order of the shapefile is maintained.
RESP_DATA_ST <- left_join(GGHB, RESP_DATA, by="SP_ID")
#Rename the columns of Observed and Expected as we did before
RESP_DATA_ST <- RESP_DATA_ST %>% dplyr::rename(O = observed, E = expected)
#Create the ID for year (time)
RESP_DATA_ST$ID.time <- RESP_DATA_ST$year - 2006
#Create the ID for space
RESP_DATA_ST$ID.space <- rep(seq(1,271),each=5)
Run the model in INLA
formula_ST_noint <- O ~ f(ID.space, model="bym2", graph=GGHB.adj,
hyper=list(prec = list(
prior = "pc.prec",
param = c(0.5 / 0.31, 0.01)),
phi = list(
prior = "pc",
param = c(0.5, 2 / 3)))) + f(ID.time,model="rw1", hyper=list(prec = list(
prior = "pc.prec",
param = c(0.5 / 0.31, 0.01))))
stBYM.model <- inla(formula=formula_ST_noint, family="poisson", data=RESP_DATA_ST, E=E, control.compute=list(dic=TRUE, waic=TRUE))
#Spatial Relative risks
RR_stBYM<-c()
for(i in 1:271){
RR_stBYM[i] <- inla.emarginal(function(x) exp(x),
stBYM.model$marginals.random$ID.space[[i]])
}
#Posterior probabilities (for spatial RR)
RR_stBYM_marg <- stBYM.model$marginals.random$ID.space[1:271]
PP_stBYM <- lapply(RR_stBYM_marg, function(x) {1-inla.pmarginal(0,x)})
#Temporal Relative risks and CI95
RR_stRW_RR<-c()
RR_stRW_lo<-c()
RR_stRW_hi<-c()
for(i in 1:5){
#Posterior mean
RR_stRW_RR[i] <- inla.emarginal(function(x) exp(x),
stBYM.model$marginals.random$ID.time[[i]])
#2.5% quantile
RR_stRW_lo[i] <- inla.qmarginal(0.025,inla.tmarginal(function(x) exp(x), stBYM.model$marginals.random$ID.time[[i]]))
#97.5% quantile
RR_stRW_hi[i] <- inla.qmarginal(0.975, inla.tmarginal(function(x) exp(x), stBYM.model$marginals.random$ID.time[[i]]))
}
RR_stRW <- data.frame(RR=RR_stRW_RR,low=RR_stRW_lo,high=RR_stRW_hi)
RR_stWR)ggplot(RR_stRW, aes(seq(2007,2011), RR)) + geom_line() + ggtitle("ST model No Int") + geom_ribbon(aes(ymin=low,ymax=high), alpha=0.2) + labs(x="year")-> Temp1
Temp1
RR_stBYM) with
ggplot2 package using the following breakpoints [min,0.4],
(0.4-0.6], (0.6-0.8], (0.8,1], (1,1.2], (1.2-1.4], (1.4-1.6], (1.6-max].
Compare this map against the map of the residual RR obtained from the
spatial model.resRR_PP_st <- data.frame(resRR=RR_stBYM,
PP=unlist(PP_stBYM),
SP_ID=RESP_DATAagg[,1])
# breakpoints
resRR_PP_st$resRRcat <- cut(resRR_PP_st$resRR, breaks=c(min(resRR_PP_st$resRR),
0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6,
max(resRR_PP_st$resRR)),include.lowest = T)
resRR_PP_st$PPcat <- cut(resRR_PP_st$PP, c(0, 0.2, 0.8, 1.00), include.lowest = TRUE)
map_RR_ST <- left_join(GGHB, resRR_PP_st, by = c("SP_ID" = "SP_ID"))
ggplot() + geom_sf(data = map_RR_ST) + aes(fill = resRRcat) +
theme_bw() + scale_fill_brewer(palette = "PuOr") +
guides(fill=guide_legend(title="RR")) + ggtitle("RR ST model") +
theme(text = element_text(size=15),
axis.text.x = element_blank(),
axis.text.y = element_blank(), plot.title = element_text(size = 12, face = "bold")
) -> p3
ggplot() + geom_sf(data = map_RR_ST) + aes(fill = PPcat) +
theme_bw() +
scale_fill_viridis(
option = "plasma",
name = "PP ST model",
discrete = T,
direction = -1,
guide = guide_legend(
title.position = 'top',
reverse = T
)) + ggtitle("PP ST model") + theme(text = element_text(size=15),
axis.text.x = element_blank(),
axis.text.y = element_blank(), plot.title = element_text(size = 12, face = "bold")
)-> p4
(p1|p2) / (p3|p4)
Spatio-temporal model: Map of the residual RRs and posterior probabilities
Now, we extend the above analysis to a separable space-time model with type I interaction:
\[ \begin{eqnarray} O_{i}|\lambda_{i} & \sim & \text{Poisson}(\lambda_{i}E_{i} ) \\ \log(\lambda_{i}) & = & \alpha + \theta_{i} + \phi_{i} + \xi_t + \gamma_t + \zeta_{it} \\ \theta_{i} & \sim & N(0, \sigma_{\theta}^2)\\ {\bf \phi} & \sim & \hbox{ICAR}({\bf W}, \sigma_{\phi}^2)\\ \gamma_t &\sim & N(0, \sigma_{\gamma}^2) \\ \xi_t & \sim & RW1(\sigma_{\xi}^2) \\ \zeta_{it} & \sim & N(0, \sigma_{\zeta}^2) \\ \alpha & \sim & \text{Uniform}(-\infty, +\infty) \\ 1/\sigma_{\theta}^2 & \sim & \text{Gamma}(1,0.001) \\ 1/\sigma_{\phi}^2 & \sim & \text{Gamma}(0.5,0.005) \\ 1/\sigma_{\gamma}^2 & \sim & \text{Gamma}(1,0.001) \\ 1/\sigma_{\xi}^2 & \sim & \text{Gamma}(0.5,0.005) \\ 1/\sigma_{\zeta}^2 & \sim & \text{Gamma}(1,0.001) \end{eqnarray} \]
INLA. Remember
that you need to create an index which goes from 1 to the length of the
dataset (i.e. the space x time)RESP_DATA_ST$ID.space.time <- seq(1,dim(RESP_DATA_ST)[1])
formula_ST_intI <- O ~ f(ID.space, model="bym2", graph=GGHB.adj,
hyper=list(prec = list(
prior = "pc.prec",
param = c(0.5 / 0.31, 0.01)),
phi = list(
prior = "pc",
param = c(0.5, 2 / 3)))) +
f(ID.time,model="rw1", hyper=list(prec = list(
prior = "pc.prec",
param = c(0.5 / 0.31, 0.01))))+
f(ID.space.time,model="iid", hyper=list(prec = list(
prior = "pc.prec",
param = c(0.5 / 0.31, 0.01))))
stIntI.BYM.model <- inla(formula=formula_ST_intI, family="poisson", data=RESP_DATA_ST, E=E, control.compute=list(dic=TRUE, waic=TRUE))
#Spatial Relative risks
RR_stIntI.BYM<-c()
for(i in 1:271){
RR_stIntI.BYM[i] <- inla.emarginal(function(x) exp(x),
stIntI.BYM.model$marginals.random$ID.space[[i]])
}
#Posterior probabilities (for spatial RR)
RR_stIntI.BYM_marg <- stIntI.BYM.model$marginals.random$ID.space[1:271]
PP_stIntI.BYM <- lapply(RR_stIntI.BYM_marg, function(x) {1-inla.pmarginal(0,x)})
#Temporal Relative risks and CI95
RR_stIntI.RW_RR<-c()
RR_stIntI.RW_lo<-c()
RR_stIntI.RW_hi<-c()
for(i in 1:5){
#Posterior mean
RR_stIntI.RW_RR[i] <- inla.emarginal(function(x) exp(x),
stIntI.BYM.model$marginals.random$ID.time[[i]])
#2.5% quantile
RR_stIntI.RW_lo[i] <- inla.qmarginal(0.025,inla.tmarginal(function(x) exp(x), stIntI.BYM.model$marginals.random$ID.time[[i]]))
#97.5% quantile
RR_stIntI.RW_hi[i] <- inla.qmarginal(0.975, inla.tmarginal(function(x) exp(x), stIntI.BYM.model$marginals.random$ID.time[[i]]))
}
RR_stIntI.RW<- data.frame(RR=RR_stIntI.RW_RR,low=RR_stIntI.RW_lo,high=RR_stIntI.RW_hi)
RR_stWR)ggplot(RR_stIntI.RW, aes(seq(2007,2011), RR)) + geom_line() + ggtitle("ST model Int I") + geom_ribbon(aes(ymin=low,ymax=high), alpha=0.2) + labs(x="year")->Temp2
Temp1 | Temp2
RR_stIntI.BYM) with
ggplot2 package using the following breakpoints [min,0.4],
(0.4-0.6], (0.6-0.8], (0.8,1], (1,1.2], (1.2-1.4], (1.4-1.6], (1.6-max].
Compare this map against the map of the residual RR obtained from the
spatial temporal model with no interaction.resRR_PP_stIntI <- data.frame(resRR=RR_stIntI.BYM,
PP=unlist(PP_stIntI.BYM),
SP_ID=RESP_DATAagg[,1])
# breakpoints
resRR_PP_stIntI$resRRcat <- cut(resRR_PP_stIntI$resRR, breaks=c(min(resRR_PP_stIntI$resRR),
0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6,
max(resRR_PP_stIntI$resRR)),include.lowest = T)
resRR_PP_stIntI$PPcat <- cut(resRR_PP_stIntI$PP, c(0, 0.2, 0.8, 1.00), include.lowest = TRUE)
map_RR_ST.IntI <- left_join(GGHB, resRR_PP_stIntI, by = c("SP_ID" = "SP_ID"))
ggplot() + geom_sf(data = map_RR_ST.IntI) + aes(fill = resRRcat) +
theme_bw() + scale_fill_brewer(palette = "PuOr") +
guides(fill=guide_legend(title="RR")) + ggtitle("RR ST model Int I") +
theme(text = element_text(size=15),
axis.text.x = element_blank(),
axis.text.y = element_blank(), plot.title = element_text(size = 12, face = "bold")
) -> p5
ggplot() + geom_sf(data = map_RR_ST.IntI) + aes(fill = PPcat) +
theme_bw() +
scale_fill_viridis(
option = "plasma",
name = "PP ST model Int I",
discrete = T,
direction = -1,
guide = guide_legend(
title.position = 'top',
reverse = T
)) + ggtitle("PP ST model Int I") + theme(text = element_text(size=15),
axis.text.x = element_blank(),
axis.text.y = element_blank(), plot.title = element_text(size = 12, face = "bold")
)-> p6
(p1|p2) / (p3|p4) / (p5|p6)
Spatio-temporal model: Map of the residual RRs and posterior probabilities
We basically see that across the different models there is no difference in the spatial residuals. Let’s now look at the ST interaction.
RESP_DATA_ST$intI<-stIntI.BYM.model$summary.random$ID.space.time$mean
RESP_DATA_ST$intI_cat <- cut(RESP_DATA_ST$intI, breaks=c(-1,-0.05,
-0.01, 0.01, 0.05, 1),include.lowest = T)
ggplot() +
geom_sf(data = RESP_DATA_ST, aes(fill = intI_cat))+ theme_bw() + scale_fill_brewer(palette = "PuOr") +
guides(fill=guide_legend(title=NULL)) +
theme(text = element_text(size=20),
axis.text.x = element_blank(),
axis.text.y = element_blank()) +
facet_wrap(~ year, ncol = 3, labeller=labeller(ID.year=c("1"="2007","2"="2008","3"="2009","4"="2010","5"="2011"))) +
labs("")
We can see that there is not clear pattern in the interactions.
dat.hyper2 <-
round(
data.frame(median = stIntI.BYM.model$summary.hyperpar[,4],
LL = stIntI.BYM.model$summary.hyperpar[,3],
UL = stIntI.BYM.model$summary.hyperpar[,5]),
digits = 3)
row.names(dat.hyper2) <-
rownames(stIntI.BYM.model$summary.hyperpar)
knitr::kable(dat.hyper2, caption = "Posterior median and 95% CrI of hyperparameters.") %>% kable_styling(bootstrap_options = "striped", full_width = F, position = "center")
| median | LL | UL | |
|---|---|---|---|
| Precision for ID.space | 7.862 | 6.277 | 9.628 |
| Phi for ID.space | 0.680 | 0.394 | 0.911 |
| Precision for ID.time | 362.430 | 72.249 | 2122.259 |
| Precision for ID.space.time | 117.504 | 95.447 | 146.324 |
dat.WAIC <- data.frame(model = c("Spatial", "SpatTemp no int", "SpatTemp typeI"),
WAIC = round(c(sBYM.model$waic$waic, stBYM.model$waic$waic, stIntI.BYM.model$waic$waic))
)
row.names(dat.WAIC) <- NULL
knitr::kable(dat.WAIC, caption = "WAIC of the fifferent models") %>% kable_styling(bootstrap_options = "striped", full_width = F, position = "center")
| model | WAIC |
|---|---|
| Spatial | 2558 |
| SpatTemp no int | 10820 |
| SpatTemp typeI | 10312 |